# calculate dot product

## Calculus dot_product

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### Function : dot_product

#### Summary :

The dot product calculator allows the calculation of the dot product of two vectors online.

Dot_product online

# Analytical definition of the scalar product

It is possible to calculate the dot product of two vectors from their coordinates. In the plan, in an orthonormal system (O,vec(i),vec(j)) , vec(u) is a vector of coordinates (x,y) and vec(v) is a vector of coordinates (x',y'), the dot product is given by the formula xx'+yy'=0.
This definition can be extended to space. In a direct orthonormal system (O,vec(i),vec(j),vec(k)), vec(u) is a vector of coordinates (x,y,z) and vec(v) is a vector of coordinates (x',y',z'), the dot product is given by the formula xx'+yy'+zz'=0.

# Property

If vec(u) and vec(v) are orthogonal, then the dot product is zero.

# Online calculation of the scalar product.

The dot product calculator allows to calculate the dot product of two vectors from their coordinates. The calculation of the scalar product online can be done with numbers or literal expressions.

## Dot product calculation from numeric coordinates.

To calculate the dot product of the following vectors vec(v) [1;5] and vec(u) [1;3], enter dot_product([1;5];[1;3]). After calculation the result 16 is returned.

## Dot product calculation from literal coordinates.

To calculate the dot product of the following vectors vec(v) [a;b-1] and vec(u) [2a;a/2], enter dot_product([a;b-1];[2a;a/2]). After calculation the result -a/2+(b*a)/2+2*a^2 is returned.

The dot product calculator allows the calculation of the dot product of two vectors online.

#### Syntax :

dot_product(vector;vector)

#### Examples :

• dot_product([1;5];[1;3]), returns 16,
• dot_product([1;5;3];[1;3;3]), returns 25
• Calculate online with dot_product (calculate dot product)